Rotation-based schedules in elementary schools to prevent COVID-19 spread: a simulation study

Rotations of schoolchildren were considered as a non-pharmacological intervention in the COVID-19 pandemic. This study investigates the impact of different rotation and testing schedules.We built an agent-based model of interactions among pupils and teachers based on a survey in an elementary school in Prague, Czechia. This model contains 624 schoolchildren and 55 teachers and about 27 thousands social contacts in 10 layers. The layers reflect different types of contacts (classroom, cafeteria, etc.) in the survey. On this multi-graph structure we run a modified SEIR model of covid-19 infection. The parameters of the model are calibrated on data from the outbreak in the Czech Republic in spring 2020. Weekly rotations of in-class and distance learning are an effective preventative measure in schools reducing the spread of covid-19 by 75–81% . Antigen testing twice a week or PCR once a week significantly reduces infections even when using tests with a lower sensitivity. The structure of social contacts between pupils and teachers strongly influences the transmission. While the density of contact graphs for older pupils is 1.5 times higher than for younger pupils, the teachers’ network is an order of magnitude denser. Teachers moreover act as bridges between groups of children, responsible for 14–18% of infections in the secondary school compared to 8–11% in the primary school. Weekly rotations with regular testing are a highly effective non-pharmacological intervention for the prevention of covid-19 spread in schools and a way to keep schools open during an epidemic.


Collection and preprocessing
The school where we collected data is located in a suburban area of a large Czech city.The school has nine grades of primary and lower secondary education (children age 6 to 15).In total, 624 students and 55 teachers were included in the data collection.The school is representative of suburban schools in the Czech republic.In particular, the school has one main building where both the primary and lower secondary grades are located.
The questionnaire had the following format: every student (or teacher) was asked to fill out every contact they meet at a particular place (e.g.classroom or lunch, cf.Table A4).They also had to indicate how often they usually meet the person.For students, contacts with students from the same class and from a different class occurred at different layers.Every student or teacher was also asked which hobby activities they attend or teach, respectively.The frequency of contacts was identified by different options in the questionnaire: several times a day, once per day, every day, sometimes, rarely.Answers differed between types of contact (e.g.every day for lunch, but once per day for break).Refer to sections C and D for complete transcripts of electronic questionnaires.
We have also used a summarized timetable that contains data of how many hours per week a teacher has in each class.Using this information, we generated edges between a teacher and all students in a class where they teach, proportionally weighted by the number of hours per week.
The contact networks were constructed from the questionnaire data as follows.The reported contacts are directed (a respondent report whom they are in contact with), but the underlying transmission network is undirected, we symmetrized the responses by the maximum value in each dyad.This also helps with imputing missing responses, as the response rate among pupils was 63% and among teachers 23%, and thus some sort of imputation of missing contacts was necessary.The social networks of pupils and teachers are presented in Table A1, two nodes in the graph are connected whenever the contact between them exists at least in one of the layers.
Table A3 presents comparison of graph densities for contacts among three main subsets of our graph -teachers, primary and secondary pupils.It can be seen that teachers contact network is very dense in comparison to the rest of contacts.Secondary pupils have about 1.5 times more contacts than primary pupils, while the contacts between younger and older pupils are relatively sparse.

Building a contact network
After the data preprocessing, we have obtained a network with 624 student nodes, 55 teacher nodes, and 27,677 edges.The edges are divided into 98 layers corresponding to four types of contacts: students in class, teacher in class, after-school clubs, and others (friendship, more contacts).The overview of layers is presented in Table A4.The frequencies of contacts and their types are then used to assess contact intensities.The intensities of contact types are taken from our epidemic model of the city, and they were obtained by survey of experts processed by the Saaty method.The contact intensity values used in our school model are presented in Table A5.For details, cf.?.The assignment of intensities and their combinations to layer types is presented in column two of Table A4.
Figure A2 and Table A6 show the results of a simulation of infection spread in a fully open school (no infection control measures) identifying the sources of infections.The majority of infections (43%) originate in class and during lunch (19%).Teachers are subject of two types of interactions (teacher-teacher and teacher-student) which together result in 17% of infections.A6.

B Results
In the following we present complete results of our three experiments that compare relative efficiency of the following measures: weekly rotations, testing, and their combination.Furthermore, we present an experiment to estimate the importance of teachers in the epidemics spread within school.For each experiment we present the results in four epidemics levels represented by average import of infected individuals.Table A7 contains numbers of individuals relative to 100 thousand inhabitants.The levels were selected to represent severe epidemics and its ratios of 50%, 25% and 10%.

Introduction
Dear students, Completing this questionnaire will help to find out which measures in schools are the most effective against the spread of coronavirus.Therefore, we ask you to think about the questions and fill them in truthfully.Every answer matters.Careful completion of the questionnaire should not take more than 10 minutes.
You cannot return to the questionnaire, so please fill in the questionnaire at once.In the questionnaire, you will fill in who you meet at school and out of school.You will fill in personal information such as name, but it will remain safe.Only one designated school staff member will work with the personal data, converting all the names to anonymous codes and then deleting the names.No one from the research team, no other school staff, or your classmates will know how you answered this questionnaire.
The questions refer to the standard times, i.e. without school closure or restrictions of other activities.The goal is to find out who you normally talk to and who you meet.

Research team
Ing. René Levinsk ý, Ph.D. Center for modeling biological and social processes Do you regularly have lunch in the school cafeteria?

School breaks
The names of students in particular classes was filled in by a designated school employee and was not accessible by researchers.
With whom from your class do you usually spend time during breaks?Your name is also in the list, there please fill in "Several times a day".
Several times a day Once in a day Sometimes Rarely Never Person 1 Person 2 Person 3 . . .With whom outside of your class do you usually spend time during breaks?Please fill in their names, grade and choose frequency how often do you meet with them.The maximum number of contacts is 10.

Outside of school
With whom from your class do you usually spend time outside of school (e.g. on the way to school, during your free time, in sports activities)?First check people, you spend time with outside of school and then fill in frequency.Your name is also on the list, there do not check the box.

Introduction
Dear school employees, The second wave of the coronavirus pandemic led to temporary school closures.The Ministry of Education, in cooperation with the academic community, is now looking for ways to open schools safely as soon as possible.By completing this questionnaire, you will provide data to help model the effects of various measures on the spread of coronavirus in schools (e.g.grade rotation scheme, afterschool club and school cafeteria closure, or class division and rotation scheme).It should take no more than 15 minutes to complete the questionnaire.You cannot return to the questionnaire, so please fill in the questionnaire at once.You will fill in personal data in the questionnaire, but it will remain safe.Only one member of the research team will work with the data with personal data, who will convert all personal information into anonymous codes and delete the personal data.Consequently, no one will be able to identify individual answers.The outputs of the project will always be presented only in aggregated form.
The questions refer to the standard times, i.e. without school closure or restrictions of other activities.The aim is to find out the contacts before pandemics.

Figure A1 :
Figure A1: The social network of pupils (left) and teachers (right).

Figure A2 :
Figure A2: Sources of infections in open school baseline scenario.The graph represents daily values of infected individuals categorized by the contact type.Numbers are sums over 1000 simulation runs.Average numbers in percent are presented in TableA6.

Figure A3 :
Figure A3: Rotation scenarios.(left) Comparison of number of infected active cases during the run.The x-axis represents days of simulation, the y-axis represents number of infections at school, mean values with standard deviation are plotted for each simulation.(right) Violin plots: all infected (cumulative over the whole run).9

Figure A4 :
Figure A4: Testing scenarios.(left) Comparison of number of infected active cases during the run.The x-axis represents days of simulation, the y-axis represents number of infections at school, mean values with standard deviation are plotted for each simulation.(right) Violin plots: all infected (cumulative over the whole run).11

Figure A5 :
Figure A5: Rotating + testing scenarios.(left) Comparison of number of infected active cases during the run.The x-axis represents days of simulation, the y-axis represents number of infections at school, mean values with standard deviation are plotted for each simulation.(right) Violin plots: all infected (cumulative over the whole run).13

Figure A6 :
Figure A6: The role of teachers.(left) Comparison of number of infected active cases during the run.The x-axis represents days of simulation, the y-axis represents number of infections at school, mean values with standard deviation are plotted for each simulation.(right) Violin plots: all infected (cumulative over the whole run).15

Table A1 :
Pupil-to-pupil contact networks -descriptive measures after-school care desk outside lunch break

Table A2 :
Teacher-to-teacher contact networks -descriptive measures

Table A3 :
Subgraph densities for interactions among three categories of nodes -teachers, primary and secondary pupils.For pupils we further differentiate contacts inside and outside of classes.Weighted density (w.d.) represents a value where contacts are weighted by their intensity and weight of the layer.

Table A4 :
Overview of the types of social contact layers.The contact intensity column refers to basic contact intensities from TableA5.

Table A5 :
Contact categories and their intensities.

Table A6 :
Percentage of sources of infections over layers in open school baseline scenario.

Table A7 :
Levels of epidemics used in our simulations.Numbers of infected calculated per 100 thousand inhabitants daily and weekly.

Table A8 :
Rotation scenarios.Percentage of numbers of infected six weeks after the start of the policy.
With whom outside of your class do you usually spend time outside of school (e.g. on the way to school, during your free time, in sports activities)?Please fill in their names, grade and choose frequency how often do you meet with them.The maximum number of contacts is 10.Filter for students who regularly have lunch in the school cafeteriaWith whom from your class do you usually spend time during lunch?First check people, you spend time with during lunch and then fill in frequency.Your name is also on the list, there do not check the box.With whom outside of your class do you usually spend time during lunch?Please fill in their names, grade and choose frequency how often do you meet with them.The maximum number of contacts is 10.Filter for students who regularly attend afterschool clubWith whom from your class do you usually spend time in the after school club?First check people, you spend time in the after school club and then fill in frequency.Your name is also on the list, there do not check the box.With whom outside of your class do you usually spend time in the after school club?Please fill in their names, grade and choose frequency how often do you meet with them.The maximum number of contacts is 10.
Ing. René Levinsk ý, Ph.D. Center for modeling biological and social processes I agree with the processing of personal data in this research project.